3.3 Statements of the second law of thermodynamics

As was already stated above, the first law of thermodynamics characterises quantitatively the processes of conversion of energy. The second law of thermodynamics characterises the qualitative side of these processes. The first law provides all that is necessary to compose the energy balance of a process. However, it gives no indications whether this or another process is feasible. Meanwhile, by far not all processes can be practically realized.

It should be stressed that the second law of thermodynamics, as well as the first, is based on experience.

In the most general form the second law of thermodynamics can be stated as follows:

Every actual spontaneous process is irreversible.

This sufficiently obvious conclusion was discussed in the preceding section. All other statements of the second law of thermodynamics are private cases of the most general statement.

In 1850 R. Clausius proposed the following statement of the second law of thermodynamics:

Heat cannot pass spontaneously from a body of lower temperature to a body of higher temperature.

W. Thomson (Lord Kelvin) in 1851 suggested the following statement:

It is impossible, by means of an inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.

M. Planck suggested the following statement:

It is impossible to construct an engine, which, when working in a complete cycle, will produce no effect other than the raising of a weight and the cooling of a heat source.

By a machine operating in a cycle is meant an engine converting heat into work in a cyclic process. Indeed, if it were possible to construct a heat engine that would simply extract heat from some source and, operating in a cycle, convert the heat into work, this would violate the previously formulated statement that a system is capable of performing work only when this system is out of equilibrium (in particular, as applied to a heat engine, when there is a difference between the temperatures of the heat source and sink in the system).

If there were no restrictions imposed by the second law of thermodynamics, this would mean that it is possible to construct a heat engine with only a heat (high temperature) source. Such an engine could operate at the expense of cooling, for instance, water in the ocean. This process could continue until the entire internal energy of the ocean would be converted into work. A heat engine which would perform in this way was given the name of a perpetual motion machine of the second kind by Wilhelm Ostwald (as distinguished from a perpetual motion machine of the first kind, operating against or violating the law of conservation of energy). In accordance with the foregoing, the statement of the second law of thermodynamics, suggested by Planck, can be modified to run as follows;

It is impossible to build a perpetual motion machine of the second kind.

It should be noted that the existence of a perpetual motion machine of the second kind does not violate the first law of thermodynamics; in fact, in this engine work would not be created from nothing, but at the expense of the internal energy of a heat source.

An important feature of heat processes should be emphasized. Mechanical work, electrical work, the work of magnetic forces, etc. can be fully converted into heat. But, as regards heat, only a fraction of it can be converted in a cyclic process into mechanical and other kinds of work; the other fraction of heat must inevitably be transferred to a low-temperature heat source (or sink).